#149 abaababaa=baabaa

Original presentation

\( \left\langle a, b \;\middle|\; a b a^{2} b a b a^{2} = b a^{2} b a^{2} \right\rangle \)

Modified presentation

\( \left\langle a, b, c, d \;\middle|\; c^{2} b a^{2} = b a c a,\; c = a b a,\; d = c a b c \right\rangle \)

Complete rewriting system

Using recursive path order (RPOCmp) with \(d < c < a < b\):

\( \begin{aligned} a b a &\rightarrow c \\ c a b c &\rightarrow d \\ c b a &\rightarrow a b c \\ b a c^{2} &\rightarrow d c \\ d a b c &\rightarrow c a b d \\ b a d &\rightarrow c a b d \\ a d a &\rightarrow c^{2} a \\ b a c a &\rightarrow d a \\ b a c d &\rightarrow d^{2} \\ b c^{2} a &\rightarrow c a b d a \\ a c a b d &\rightarrow c d \\ a d c &\rightarrow c^{3} \\ d b a &\rightarrow c^{2} b c \\ b c^{3} &\rightarrow c a b d c \\ b c d &\rightarrow d a b d \\ a d^{2} &\rightarrow c^{2} d \\ c^{2} d a &\rightarrow d c a \\ c^{3} a b d &\rightarrow d^{2} \\ c^{2} d c &\rightarrow d c^{2} \\ b c^{2} d &\rightarrow d c^{2} a b d \\ c^{2} d^{2} &\rightarrow d c d \\ b d c a &\rightarrow d c^{2} a b d a \\ b d c^{2} &\rightarrow d c^{2} a b d c \\ b d c d &\rightarrow d c d c^{2} a b d \\ b d^{2} &\rightarrow d c d a b d \end{aligned} \)